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We prove the existence of a $B$-continuous viscosity solution for a class ofinfinite dimensional semilinear partial differential equations (PDEs) usingprobabilistic methods. Our approach also yields a stochastic representationformula for the solution in terms of a scalar-valued backward stochasticdifferential equation. The uniqueness is proved under additional assumptionsusing a comparison theorem for viscosity solutions. Our results constitute thefirst nonlinear Feynman-Kac formula using the notion of $B$-continuousviscosity solutions and thus introduces a framework allowing forgeneralizations to the case of fully nonlinear PDEs.

Semilinear Feynman-Kac Formulae for $B$-Continuous Viscosity Solutions